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SUMMARY

The discussion focuses on calculating the number of active cesium nuclei in an 800-gram fish caught near the Fukushima nuclear power plant, which contains 7.4 megabecquerels per kilogram of radioactive cesium-137 (Cs-137). The half-life of Cs-137 is approximately 30 years, and the initial equation used for activity, A(t), was misapplied by assuming a decay time of one year, leading to unit mismatches between years and disintegrations per second (Bq). Proper understanding of the half-life and unit conversions is crucial for accurate calculations in radioactive decay scenarios.

PREREQUISITES
  • Understanding of radioactive decay and half-life concepts
  • Familiarity with the unit becquerel (Bq) for measuring radioactivity
  • Basic knowledge of nuclear physics and cesium-137 properties
  • Ability to perform unit conversions in scientific calculations
NEXT STEPS
  • Learn about radioactive decay equations and their applications
  • Study the properties and behavior of cesium-137 in environmental contexts
  • Explore unit conversion techniques for scientific measurements
  • Investigate the implications of radioactive contamination in marine life
USEFUL FOR

Students in nuclear physics, environmental scientists, and anyone involved in assessing the impact of radioactive materials on ecosystems will benefit from this discussion.

tomcajot
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Homework Statement
Near the Fukushíma nuclear power plant, a fish was caught with a record amount of radioactive 137-Cs of 7.4 megabecquerels per kilogram. Calculate the number of active cesium nuclei in an 800 gram fish.
Relevant Equations
(Don't know how to add LaTeX, the relevant equations will be in the picture in the solution attempt)
Screenshot 2021-12-08 at 17.34.30.png
 
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tomcajot said:
Homework Statement:: Near the Fukushíma nuclear power plant, a fish was caught with a record amount of radioactive 137-Cs of 7.4 megabecquerels per kilogram. Calculate the number of active cesium nuclei in an 800 gram fish.
Relevant Equations:: (Don't know how to add LaTeX, the relevant equations will be in the picture in the solution attempt)

View attachment 293787
Hi @tomcajot and welcome to PF.

Here are some points to consider…

Your equation for A(t) is used to find the activity after a given time (t) has elapsed. This isn’t really appropriate in this question (Though the equation can be used if you realize what value to use for elapsed time.)

You have used ‘30’ as the half-life of Cs-137. This is the approximate half-life of Cs-137 in years, Your working implies that you have take t=1 year – i.e. you have assumed the sample has been decaying for 1 year. (The fish will have gone off by then.)

You have also used the half-life in years in an equation where the activity is in Bq (disintegrations per second). So you have a problem with mismatched units.
 

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